Whisk the cornstarch into the vegetable broth. Melt the butter over medium heat in a saute pan, and then add the chicken broth mixture, red peppers and garlic. Simmer 30 minutes. *Pour hot mixture into blender and blend until smooth to make red pepper sauce. While the pepper sauce is simmering, begin the polenta.
For the Polenta:
Combine vegetable stock and cream in a large heavy saucepan. Heat to a gentle boil over medium heat, being careful not to burn. While whisking constantly, gradually add the cornmeal. Once cornmeal is incorporated, keep heat low and continue to whisk until mixture is slightly thickened and creamy. Stir in Parmesan, and season with pepper. (Since Parmesan is salty, add salt only if needed). Set aside in a warm place.
For the Ragout:
Heat oil in a saute pan. Saute onion, garlic, carrot, zucchini, yellow squash, and eggplant, until they begin to soften. Stir in tomato paste, chopped fresh parsley, thyme, and let cook until flavors integrate, about 10 more minutes. Add olives and heat through. Season with salt and pepper, as needed. Remove from heat and stir in fresh tomato. Let sit to rest.
Place cheese polenta onto serving plate, making a well in the center. Top with vegetable ragout in the center, and spoon red pepper coulis over top. Garnish with fresh basil.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.